Evaluating South African Fiscal and Monetary Policy Trade‐offs Using a Wavelet‐Based Model

• Published date: 01 December 2018
• Author: David Hudgins,Patrick M. Crowley
• DOI: http://doi.org/10.1111/saje.12206
• Date: 01 December 2018

© 2018 Economic Society of Sout h Africa.

South African Journal of Economics Vol. 86:4 December 2018

doi : 10.1111/ saje .122 06

401

EVALUATING SOUTH AFRICAN FISCAL AND MONETARY

POLICY TRADE-OFFS USING A WAVELET-BASED MODEL

PATRICK M. CROWL EY* AND DAVID HUD GINS†

Abstract

The balance between South African fiscal and monetary policy in an open economy context poses

some interesting questions for policymakers: questions such as whether more aggressive monetary

or fiscal policy will likely deliver better growth prospects in the short and medium run, and what

will the consequences be for the real exchange rate and for inflation? This research applies wavelet

analysis to post-apartheid South African quarterly macroeconomic data, and uses the decomposition

to simulate a large state-space linear-quadratic tracking model. We find that restricted fiscal policy

is the best option to realise growth, leading to lower interest rates, lower inflation, real exchange

depreciation and improved trade balances compared to restricted monetary policy.

JEL Classification: C61; C63; C88; E52; E61; F47

Keywords: Discr ete wavelet analysis, fiscal policy, mon etary policy, optimal control, South Af rica

1. INTRODUCTION

The South African e conomic policy mix is truly u nique – it is a developing country with

a fiscal policy that is heavily weighted towards transfer payments for development pur-

poses, a monetary policy that is run by an operationally independent central bank with

a focus on inflation and macroprudential stability, and an exchange rate policy that is

largely benign (but with some capital controls for domestic residents), with no specific

targets for the exchan ge rate.1 The South African c entral bank, the South Africa n Reserve

Bank (SARB), has a conventional central ba nk mandate with a focus on price stability by

the use of a targeted band for the inf lation rate. Both the nominal exchange rate and its

real counterpart are important for growth, as South Africa is a relatively open economy.

So it would not make sense to model the economy as closed, therefore, in that it is a

commodity exporting country, so the exchange rate is certainly an important factor in

determining economic growth.

1 See Address by Lesetja Kganyago, Governor of the South African Reserve Bank at the Annual

Convention of the South African Chamber of Commerce and Industry (SACCI), Emperors

Palace, Johannesburg , 20 October 2016. Accessible online at https://www.bis.org/review/

r16102 4h .pd f.

* Corresponding author: Depa rtment of Decision Sciences and Economics, College of Busine ss,

Texas A & M University – Corpus Christi, OC NR 373, 6300 Ocean Drive, Cor pus Christi, TX

78412, USA. E-mail: patrick .crowley@tamucc.edu

† Department of Decision Sciences a nd Economics, College of Business, Texas A & M

University - Corpus Christ i, Texas, USA.

South African Journal

of Economics

South African Journal of Economics Vol. 86:4 December 2018402

© 2018 Economic Society of Sout h Africa.

This paper is an extension of previous work using a conventional accelerator model,

but expanded to consider an open economy context, and tailored to specifically model

the South African m acroeconomy. It builds on Kendrick and Shoukry (2014), which first

simulated jointly optimal U.S. fiscal and monetary policy within a closed economy ac-

celerator model. The previous work done on closed economies in Crowley and Hudgins

(2015), Crowley and Hudgins (2017a, 2017b) employed a similar strategy of using a

wavelet technique called the Max imal Overlap Discrete Wavelet Transform (MODWT)

to obtain the time-frequency domain cyclical decomposition of quarterly U.S. or eu-

ro-area GDP component data, and then simulated optimal fiscal policy or jointly opti-

mal fiscal and monetary policy.

This is the fi rst research to simulate both monetary and fisc al policy in an open-econ-

omy optimal control framework based on discrete wavelet analysis, and this paper fo-

cuses on the policy implications rather than the model derivation, which is detailed in

a companion paper (Hudgins and Crowley, 2018a). In simulating the resulting model,

the research highlights the trade-offs bet ween fiscal and monetary policy, while inte-

grating SARB monetary policy objectives regarding inflation and then clarifying the

implications for the South African rea l exchange rate and the trade balance. In short,

the research provides the most complete picture of macroeconomic policy trade-offs in a

time-frequency domain setting in the context of South Africa to date.

Section 2 examines the MODWT wavelet decomposition of the data in the time-fre-

quency domain. Section 3 contains the model derivation, and then Section 5 presents

simulations using various policy assumptions. Section 6 then concludes.

2. MODWT WAVELET A NALYSIS, DATA AND BACKGROUND

As detailed in Crowley (2007), cyclical information can be extracted from a time series

using time-frequency domain methods, which includes the technique used here, namely

discrete wavelet analysis. Using Ma llat’s pyramid algorithm and multiresolutional a naly-

sis, any discrete variable x at time instant k, Zk, permits the following decomposition:

The dj,k terms are wavelet detail “cry stals,” j = 1,…, J; SJ,k is a trend component, called

the wavelet “smooth” which captures any residual which by definition includes longer

cycles not captured by the detail “crystals” plus any trend, and J represents the number

of scales (frequency bands). There are a plethora of different wavelet filter functions

used in discrete wavelet analysis to direct a filtering process that utilises pairs of low

pass and high pass filters, but for this paper we utilise the asymmetric Daubechies 4-tap

(D4) wavelet function. This wavelet funct ion has performed well on GDP data for other

countries, as business and growth cycles in general tend to be asy mmetric in nature, and

the choice of wavelet function tends not to change the qualitative results and with mac-

roeconomic data only has a minor impact on the quantitative results. Lastly, we employ

the MODWT as our method of time-frequency decomposition.

Although widely accepted in the physical and medical sciences, wavelet analysis has

been slow to enter the toolbox of methods used in empirical economics, but this is now

being addressed by numerous recent contributions. Examples include Aguiar-Conraria

(1)

Zk≈SJ,k+dJ,k+dJ−1,k+... +d1, k